ATLAS [1]}, [2]} and CMS [3]}, [4]} have already perform searches for the \(Z^{\prime }\)  by the dilepton signature. Since \(Z^{\prime }\rightarrow \mu ^+\mu ^-\)  is the only dilepton final states, the CMS limit on \(\mu ^+\mu ^-\)  is more suitable for this model. The limit is on the ratio
\(R_\sigma =\frac{\sigma (pp\rightarrow Z^{\prime }+X\rightarrow \mu ^+\mu ^-+X)}{\sigma (pp\rightarrow Z+X\rightarrow \mu ^+\mu ^-+X)}.\) 
